How should we redifine function Fr 6r 1 1r 1 so its conti

How should we redifine function F(r) = 6^r + 1 -1/r + 1 so it\'s continuous at -1?

Solution

f(r)=[b^r+1 -1]_/(r+1)

lim_r->-1f(r)

=lim_r->-1 ([b^r+1 -1]_/(r+1))

we get 0/0 form, so apply lhospitals rule differentiate numerator and denominator with respect to r

=lim_r->-1 ([b^r+1ln(b) -0]_/(1+0))

=lim_r->-1 (b^r+1ln(b))

=(b^-1+1ln(b))

=(b⁰ln(b))

=1*ln(b)

=ln(b)

function will be continous at r =-1 if function is defined as f(r)=ln(b) when r =-1